Shock Tube simulation using Converge CFD

Introduction : 

           The shock tube is an instrument used to replicate and direct blast waves at a sensor or a model in order to simulate actual explosions and their effects, usually on a smaller scale.  Shock tubes can also be used to study aerodynamic flow under a wide range of temperatures and pressures that are difficult to obtain in other types of testing facilities. 

                                                                                  Fig - Experimental Setup 

A simple shock tube is a tube, rectangular or circular in cross-section, usually constructed of metal, in which a gas at low pressure and a gas at high pressure are separated using some form of diaphragm. The diaphragm suddenly bursts open under predetermined conditions to produce a wave propagating through the low pressure section. The shock that eventually forms increases the temperature and pressure of the test gas and induces a flow in the direction of the shock wave. Observations can be made in the flow behind the incident front or take advantage of the longer testing times and vastly enhanced pressures and temperatures behind the reflected wave. The bursting diaphragm produces a series of pressure waves, each increasing the speed of sound behind them, so that they compress into a shock propagating through the driven gas. This shock wave increases the temperature and pressure of the driven gas and induces a flow in the direction of the shock wave but at lower velocity than the lead wave. Simultaneously, a rarefaction wave, often referred to as the Prandtl-Meyer wave, travels back in to the driver gas.

Objective : 

1. To simulate a Shock tube : transient simulation. 

2. Understand the pressure and temperature history in "regions" of entire domain created through converge cfd. 

3. AMR with sgs parameter and explanation of cell count. 

Geometry in Converge studio : 

This geometry is imported in converge and separated into two wall boundaries which represents two regions, high pressure and low pressure i.e purple and white respectively. Boundary flagging done that way. There is no diaphragm in between. It will be simulated using events based on the regions from converge tools.

Meshing : 

Grid size 0.0015 m is set as base size observed in the first figure and the final time step mesh shown next is the result of adaptive mesh refinement with sgs parameter 0.001 and 3 embed scale with permanent timing type for N2 species.  

                                                                                Base Mesh

                                                                        Mesh at Final time step. 

Cell count plot : 

The total cell count plot shows the variation of mesh sizes as a function of time during the entire simulation of 0.003 seconds. The sudden spike at 0.001 second is observed as that is the timing set in the events tool for the diaphragm to burst i.e the two regions to mix and when the simulation begins without any delay the high pressure region pushes the low pressure region behind due to which the AMR sgs gets activated and the variation of plot shows that. The sudden decrease in mesh size is when the reflected pressure pushes it back and in the simulation the bigger cell sizes can seen which is shown ahead and simularly they increase again not going above 200k as that is defined as max limit. 

Case Setup : 

1. Application type : Time Based

2. Material : Air mixture ( Gas simulation) 

3. Gas Species : 02 , N2 .

4. Solver : Transient solver , Fully Hydrodynamic. 

5. Gas flow solver : Compressible.

6. Misc : Momentum , Energy on 

7. Simulation Time parameters : 

i. Start 0 s

ii. End : 0.003s. 

iii. Initial Time-step : 1e-9s

iv. minimum Time-step  1e-9s

v. Max time-step 1s.

8. Solver scheme : Piso algorithm : Density Based

9. Boundary Conditions : 

i. Boundary 1 : High pressure : Wall ; stationary ; slip. Temp 300 k

ii. Boundary 2 : Low pressure : Wall ; stationary ; slip. Temp 300 k

12. Regions & Initialization : 

13 Region 0 High pressure: Pressure 600000 pa ; Temp : 300 K ; Species : N2 100% .

13.1 Region 1 Low pressure: Pressure 101325 pa ; Temp : 300 K ; Species : O2 100% .

13.2 Events : 

14. Turbulence Model : RNG K-epsilon

15. Output Files : Time interval for writing 3D output data files : 1e-5s.

16. Max restart files saved : 3 

17. Grid control : As mentioned in Meshing.

Solution and Post processing : 

Mass fraction N2 Contour : Shock tube

As the diaphragm breaks the high pressure region N2 pushes the O2 low pressure region then the low pressure region reflects back and pushes it towards N2 region. This shock waves keeps moving back and forth as the waves have different pressures and due to which this occurs and after a while if the simulation is ran for more time the pressure eventually settles and converges to a value. 

AMR Animation of mass_frac N2. 

Pressure : 

The High pressure region is 600k pa and as seen from plot the simulation never reaches that pressure. The pressure as soon as the diaphragm breaks at 0.001 seconds increases upto 360k pa thats when the high pressure region pushes the low pressure region and while its sort of pushing and disolving, until reflected wave can occur we see still pressure and slight drop in plot and when the reflection pressure (shock) wave is generated on the low pressure region the pressure rises. Similarly both the regions generate a sine wave like structure with their shock waves. This pressure eventually dissolves into steady value when simulation is ran for more time steps. 

Pictoral representation of animation : 

                                1. 

                               2. 

                              3. 

Temperature :

Similarly with temperature contour & plot a continual sinwave type plot is seen it happens due to continous increase and decrease in temperature as shocks are propogating forward and backwards. We see the highest temperature remains at thre high pressure region from the contour and still as shock propogates it increaes the temperature of lower region aswell. This happens due to increadible pressure difference @ initial conditions and diaphragm burst and thus shocks develop these properties. The plot depicts average total temperature for both regions. 

Velocity contour animation : 

The velocity increases sharp as diaphragm burst and increases forth and decreases back and vice versa, such waves create shock patterns like diamond shock pattern observed near the low pressure region. 

keywords - SHOCK, CFD, PARAVIEW, CONVERGE, CAE

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